Question

Evalute 997^3 by using algebric identities.​

Answer 1

997³ = (1000 - 3)³

(a-b) ³ = (a-b)(a²-2ab + b²)

here a = 1000 and b = 3

(1000 - 3)³ = (1000 - 3) (1000²- 2×1000×3 + 3²)

(1000 - 3)³ = (1000 - 3)(1000000 - 6000 + 27)

(1000 - 3)³ = (1000 - 3) ×994027

(1000 - 3)³ = 994027 × 1000 - 994027 × 3

(1000 - 3)³  = 994027000 - 2982081

(1000 - 3)³  = 991044919